Assuming that the earth is spherically symmetrical and has a substantially uniform mass distribution, the size, shape and orientation of the orbit of an earth satellite can be completely described by specifying six independent variables, which are conventionally called "orbital elements". The orbital elements of an earth satellite can be specified in terms of a three-dimensional, rectangular, cartesian coordinate system defined by unit vectors I, J and K with a geocentric origin, where the unit vectors I and J lie in a so-called "fundamental plane" that coincides with the equatorial plane of the earth, and where the unit vector K is perpendicular to the fundamental plane and points to the north pole of the earth. In general, the orbit of an earth satellite traces an elliptical path in a plane (called the "orbital plane") that intersects the fundamental plane. Furthermore, an earth satellite generally has an angular momentum (i.e., a spin) represented by a vector h, which is inclined at an angle with respect to the unit vector K.
In FIG. 1, the orbital elements of an earth satellite are illustrated as follows:
(1) the semi-major axis of the elliptical orbit of the satellite, which is a constant defining the size of the orbit; PA1 (2) the eccentricity, e, of the elliptical orbit of the satellite, which is a constant defining the shape of the orbit; PA1 (3) the inclination, i, of the satellite's orbital plane, which is the angle between the unit vector K and the angular momentum vector h; PA1 (4) the longitude of the ascending node, .OMEGA., which is the angle in the fundamental plane between the unit vector 1 and the line in the fundamental plane at which the orbit of the satellite crosses through the fundamental plane (i.e., PA1 (5) the argument of perigee, .OMEGA., which is the angle in the orbital plane of the satellite between the ascending node and the point of perigee (i.e., the point in the orbit of the satellite that is closest to the earth) measured in the direction of the satellite's motion; and PA1 (6) the true anomaly at epoch, .nu..sub.O, which is the angle in the orbital plane of the satellite between perigee and the position of the satellite at a particular time. PA1 1) a first set of one or more satellites for delivery to a designated first orbit in a first orbital plane, and PA1 2) a second set of one or more satellites for delivery to a designated second orbit in a second orbital plane,
the "line of nodes", n) as the satellite travels in a northerly direction measured counterclockwise when viewed from the north side of the fundamental plane;
In reality, the earth is not spherically symmetric, but is bulged at the equator, flattened at the poles and is generally asymmetric in mass distribution. This asymmetricity of the earth produces perturbative accelerations on a satellite that is intended to remain in a designated orbital plane. Such perturbative accelerations cause the satellite's actual orbital plane to change over time from the designated orbital plane.
Various satellite communication networks have been proposed, which would require that a plurality of satellites be transported to different planar orbits. In FIG. 2, a technique that has been previously proposed for dispensing two different sets of satellites into two correspondingly different planar orbits from a single launch vehicle is illustrated. As indicated in FIG. 2, a single launch vehicle (e.g., a rocket) dispenses a first set comprising one or more satellites into a designated first orbit in a first orbital plane; and the launch vehicle is then accelerated (with a concomitant expenditure of fuel) directly to a second orbital plane at which a second set comprising one or more satellites is dispensed into a designated second orbit in the second orbital plane.
The technique for accelerating the launch vehicle directly from the first orbital plane to the second orbital plane, as illustrated in FIG. 2, does not make use of the perturbative accelerations affecting the launch vehicle when the launch vehicle is in orbit in the first orbital plane.